2.7 Two-Variable Inequalities Graphing Linear Inequalities Graphing Absolute-Value Inequalities
1) Graphing Linear Inequalities The graph of a linear inequality is a region of the coordinate plane that is bounded by a line
1) Graphing Linear Inequalities What it shows… the values on the coordinate plane that apply to the function What an equation looks like…
1) Graphing Linear Inequalities What it shows… the values on the coordinate plane that apply to the function What an equation looks like… Inequality symbol Slope y-intercept
1) Graphing Linear Inequalities What linear inequality graphs look like… 1) boundary line (solid or dashed) 2) shaded area (above or below the boundary line)
1) Graphing Linear Inequalities A dashed boundary line means the line is NOT part of the solution The shading is ABOVE the boundary line if the equation is of the form y > OR y > y < OR y >
1) Graphing Linear Inequalities A solid boundary line means the line IS part of the solution The shading is BELOW the boundary line if the equation is of the form y < OR y < y < OR y >
1) Graphing Linear Inequalities Example 1: Graph the inequality y < 2x + 2
1) Graphing Linear Inequalities Remember… y = mx + b Example 1: Graph the inequality y < 2x + 2
1) Graphing Linear Inequalities Remember… y = mx + b Example 1: Graph the inequality y < 2x + 2 y-int = 2 m = 2
1) Graphing Linear Inequalities Example 1: Graph the inequality y < 2x + 2 y-int = 2 m = 2
1) Graphing Linear Inequalities Example 1: Graph the inequality y < 2x + 2 y-int = 2 m = 2
1) Graphing Linear Inequalities Example 1: Graph the inequality y < 2x + 2 y-int = 2 m = 2
1) Graphing Linear Inequalities Example 1: Graph the inequality y < 2x + 2 y-int = 2 m = 2 y < DASHED line
1) Graphing Linear Inequalities Example 1: Graph the inequality y < 2x + 2 y-int = 2 m = 2 y < SHADE BELOW the line
1) Graphing Linear Inequalities Example 2: Write an inequality for the graph below.
1) Graphing Linear Inequalities Example 2: Write an inequality for the graph below. y = mx + b y –int = m = inequality type
1) Graphing Linear Inequalities Example 2: Write an inequality for the graph below. y = mx + b y –int = m = inequality type
1) Graphing Linear Inequalities Example 2: Write an inequality for the graph below. y = mx + b y –int = -3 m = inequality type
1) Graphing Linear Inequalities Example 2: Write an inequality for the graph below. y = mx + b y –int = -3 m = -3/2 inequality type >
1) Graphing Linear Inequalities Example 2: Write an inequality for the graph below. y –int = -3 m = -3/2 inequality type > Sub into y > mx + b
1) Graphing Linear Inequalities Example 2: Write an inequality for the graph below. y –int = -3 m = -3/2 inequality type > Sub into y > mx + b y > -3x/2- 3
Homework p.104 #1, 5, 7, 20, 21, 23, 26, 37, 38 Don’t forget… Quiz TUESDAY Test FRIDAY
2) Absolute Value Inequalities Graph the absolute value function then shade above OR below
2) Absolute Value Inequalities Graph the absolute value function then shade above OR below Solid line…y <, y> Dashed line…y<, y> Shade above y>, y> Shade below…y<, y<
2) Absolute Value Inequalities Example 1: Graph y < |x – 2| + 3
2) Absolute Value Inequalities Example 1: Graph y < |x – 2| + 3 DASHED line Shade BELOW slope = 1 Vertex = (2, 3)
2) Absolute Value Inequalities Example 1: Graph y < |x – 2| + 3 slope = 1 DASHED line Shade BELOW Vertex = (2, 3)
2) Absolute Value Inequalities Example 1: Graph y < |x – 2| + 3 slope = 1 DASHED line Shade BELOW Vertex = (2, 3)
2) Absolute Value Inequalities Example 1: Graph y < |x – 2| + 3 slope = 1 DASHED line Shade BELOW Vertex = (2, 3)
2) Absolute Value Inequalities Example 1: Graph y < |x – 2| + 3 slope = 1 DASHED line Shade BELOW Vertex = (2, 3)
2) Absolute Value Inequalities Example 1: Graph y < |x – 2| + 3 slope = 1 DASHED line Shade BELOW Vertex = (2, 3)
2) Absolute Value Inequalities Example 2: Graph –y + 1 < -2|x + 2|
2) Absolute Value Inequalities Example 2: Graph –y + 1 < -2|x + 2| -y < -2|x + 2| - 1 y > 2|x + 2| + 1 -y so CHANGE the direction of the inequality
2) Absolute Value Inequalities y > 2|x + 2| + 1
2) Absolute Value Inequalities y > 2|x + 2| + 1 Slope = 2 Solid line Shade above Vertex = (-2, 1)
2) Absolute Value Inequalities y > 2|x + 2| + 1
2) Absolute Value Inequalities y > 2|x + 2| + 1
2) Absolute Value Inequalities y > 2|x + 2| + 1
2) Absolute Value Inequalities y > 2|x + 2| + 1
2) Absolute Value Inequalities Example 3: Write an equation for the graph below.
Homework p.104 #11-13, 22, 30, 39-42 Reminders… Quiz TUESDAY (2.5, 2.6, first half 2.7) Review WEDNESDAY, THURSDAY Test FRIDAY (Chapter 2 ONLY) Extra-help WEDNESDAY at LUNCH